Title: Composite structured mesh generation with automatic domain decomposition in complex geometries Authors
|Zhang, Yaoxin -|
|Jia, Yafei -|
|Wang, Sam -|
|Altinakar, Mustafa -|
Submitted to: Engineering Applications of Computational Fluid Mechanics
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: October 8, 2012
Publication Date: July 1, 2013
Citation: Zhang, Y., Jia, Y., Wang, S.S., Altinakar, M. 2013. Composite structured mesh generation with automatic domain decomposition in complex geometries. Engineering Applications of Computational Fluid Mechanics. 7(1):90-102. Interpretive Summary: Challenge still remains for quality structured mesh generation in complex domains of arbitrary shapes in Computational Fluid Dynamics (CFD) analysis. In complex geometries, one big difficulty of structured mesh generation lies in the distribution of mesh nodes along the domain boundaries, because it directly controls the global mapping between the computational mesh and the physical domains, and poor distribution results in meshes with poor quality. To alleviate this difficulty, the multi-block method, an approach that divides a complicated domain into several sub-domains (blocks) with simpler shapes, is often used. In this study, the multi-block method is only used for mesh generation, which implies that mesh is not only block structured but also globally structured after assembling. The key of multi-block method is the domain decomposition. Appropriate decomposition can greatly improve mesh quality and generation efficiency. Unfortunately, domain decomposition is also the most difficult and time-consuming step. In CFD analysis, a typical mesh generation takes up to more than one half of labor hours for a case study. To improve the efficiency and reduce difficulties of mesh generation, automating the domain decomposition process becomes crucial. In the current study, a novel automatic domain decomposition algorithm for 2D complex geometries is proposed. The proposed decomposition algorithm is based on the initial Delaunay Triangulation (IDT) of the refined boundary of a domain. The shortest-virtual-edge Rule (SVE Rule) is devised to decompose the geometrically complex domains with curved complicated boundaries. According to the SVE Rule, the SVEs of the effective concave points are identified as the candidates of block interface lines. Blocks are extracted from the APLs of interface lines and organized in a hierarchical structure. Examples and application have demonstrated that the present algorithm is easy to implement and effective in decomposing any arbitrary-shaped complex domains without islands or holes (inner boundaries) into multi-blocks with simpler shapes. Currently the proposed algorithm is only devoted to 2D single-connected domains without islands or holes. It can be further improved by refining the current existing rules (the SVE Rule) and devising new complementary rules in order to handle more complicated domains, i.e., multi-connected domains with islands or holes (inner boundaries). Extension of the present algorithm to 3D domains would be difficult, which needs more researches in the future.
Technical Abstract: This paper presents a novel automatic domain decomposition method to generate quality composite structured meshes in complex domains with arbitrary shapes, in which quality structured mesh generation still remains a challenge. The proposed decomposition algorithm is based on the analysis of an initial Delaunay triangulation on the closed boundary of the computational domain. The virtual edges with the so-called shortest effective length of the effective concave points are identified as candidates of the interface line between neighboring blocks. As demonstrated by examples and application, the proposed algorithm is capable of effectively decomposing complex domains without holes or islands (inner boundaries) into simpler patched blocks and thus significantly alleviated the difficulties of structured mesh generation in those domains.